In this work, we present an application of symbolic control and contract based design techniques to vehicle platooning. We use a compositional approach based on continuous-time assume-guarantee contracts. Each vehicle in the platoon is assigned an assume-guarantee contract; and a controller is synthesized using symbolic control to enforce the satisfaction of this contract. The assume-guarantee framework makes it possible to deal with different types of vehicles and asynchronous controllers (i.e controllers with different sampling periods). Numerical results illustrate the effectiveness of the approach.
{"title":"Contract based Design of Symbolic Controllers for Vehicle Platooning","authors":"Adnane Saoud, A. Girard, L. Fribourg","doi":"10.1145/3178126.3187001","DOIUrl":"https://doi.org/10.1145/3178126.3187001","url":null,"abstract":"In this work, we present an application of symbolic control and contract based design techniques to vehicle platooning. We use a compositional approach based on continuous-time assume-guarantee contracts. Each vehicle in the platoon is assigned an assume-guarantee contract; and a controller is synthesized using symbolic control to enforce the satisfaction of this contract. The assume-guarantee framework makes it possible to deal with different types of vehicles and asynchronous controllers (i.e controllers with different sampling periods). Numerical results illustrate the effectiveness of the approach.","PeriodicalId":131076,"journal":{"name":"Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132822409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Session details: Temporal Logic and its Applications","authors":"N. Ozay","doi":"10.1145/3258030","DOIUrl":"https://doi.org/10.1145/3258030","url":null,"abstract":"","PeriodicalId":131076,"journal":{"name":"Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121097618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Finding the minimal bit rate needed for state estimation of a dynamical system is a fundamental problem in control theory. We present two notions of topological entropy, one to lower bound the bit rate needed to estimate the state of a nonlinear dynamical system, with unknown bounded inputs, up to a constant error ε. The other is to do the same but to estimate the state of a switched system with unknown switching signal up to an error that is bounded by ε for τ seconds after each switch and then decays exponentially at a rate of α till the next switch. Since computation of entropy is hard in general, we present upper bounds on both notions of entropy. Finally, we present preliminary results on the relation between the two notions. Note that most of the ideas presented in this abstract are from our papers [4] and [5].
{"title":"Recent Results in State Estimation of Dynamical Systems with Inputs under Bandwidth Constraints","authors":"Hussein Sibai, S. Mitra","doi":"10.1145/3178126.3187002","DOIUrl":"https://doi.org/10.1145/3178126.3187002","url":null,"abstract":"Finding the minimal bit rate needed for state estimation of a dynamical system is a fundamental problem in control theory. We present two notions of topological entropy, one to lower bound the bit rate needed to estimate the state of a nonlinear dynamical system, with unknown bounded inputs, up to a constant error ε. The other is to do the same but to estimate the state of a switched system with unknown switching signal up to an error that is bounded by ε for τ seconds after each switch and then decays exponentially at a rate of α till the next switch. Since computation of entropy is hard in general, we present upper bounds on both notions of entropy. Finally, we present preliminary results on the relation between the two notions. Note that most of the ideas presented in this abstract are from our papers [4] and [5].","PeriodicalId":131076,"journal":{"name":"Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127101764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Rajhans, S. Avadhanula, A. Chutinan, P. Mosterman, Fu Zhang
Simulink and Stateflow are tools for Model-Based Design that support a variety of mechanisms for modeling hybrid dynamics. Each of these tools has different strengths. In this paper, a new modeling construct is presented that combines these strengths to enable graphical modeling of hybrid dynamics within a single Stateflow chart. A new type of Stateflow state that acts as a Simulink subsystem is developed to facilitate graphical modeling of continuous dynamics using Simulink blocks inside Stateflow. Remote textual and graphical state access using new state-accessor blocks enables continuous states to be used in transition guards and reset actions. Key features of this new formalism are illustrated using various examples with hybrid dynamics.
{"title":"Graphical Modeling of Hybrid Dynamics with Simulink and Stateflow","authors":"A. Rajhans, S. Avadhanula, A. Chutinan, P. Mosterman, Fu Zhang","doi":"10.1145/3178126.3178152","DOIUrl":"https://doi.org/10.1145/3178126.3178152","url":null,"abstract":"Simulink and Stateflow are tools for Model-Based Design that support a variety of mechanisms for modeling hybrid dynamics. Each of these tools has different strengths. In this paper, a new modeling construct is presented that combines these strengths to enable graphical modeling of hybrid dynamics within a single Stateflow chart. A new type of Stateflow state that acts as a Simulink subsystem is developed to facilitate graphical modeling of continuous dynamics using Simulink blocks inside Stateflow. Remote textual and graphical state access using new state-accessor blocks enables continuous states to be used in transition guards and reset actions. Key features of this new formalism are illustrated using various examples with hybrid dynamics.","PeriodicalId":131076,"journal":{"name":"Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131719724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Session details: Stochastic Systems","authors":"P. Prabhakar","doi":"10.1145/3258024","DOIUrl":"https://doi.org/10.1145/3258024","url":null,"abstract":"","PeriodicalId":131076,"journal":{"name":"Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129715108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jie An, N. Zhan, Xiaoshan Li, Miaomiao Zhang, W. Yi
Extended Linear Duration Invariants (ELDI), an important subset of Duration Calculus, extends well-studied Linear Duration Invariants with logical connectives and the chop modality. It is known that the model checking problem of ELDI is undecidable with both the standard continuous-time and discrete-time semantics [12, 13], but it turns out to be decidable if only bounded execution fragments of timed automata are concerned in the context of the discrete-time semantics [36]. In this paper, we prove that this problem is still decidable in the continuous-time semantics, although it is well-known that model-checking Duration Calculus with the continuous-time semantics is much more complicated than the one with the discrete-time semantics. This is achieved by reduction to the validity of Quantified Linear Real Arithmetic (QLRA). Some examples are provided to illustrate the efficiency of our approach.
{"title":"Model Checking Bounded Continuous-time Extended Linear Duration Invariants","authors":"Jie An, N. Zhan, Xiaoshan Li, Miaomiao Zhang, W. Yi","doi":"10.1145/3178126.3178147","DOIUrl":"https://doi.org/10.1145/3178126.3178147","url":null,"abstract":"Extended Linear Duration Invariants (ELDI), an important subset of Duration Calculus, extends well-studied Linear Duration Invariants with logical connectives and the chop modality. It is known that the model checking problem of ELDI is undecidable with both the standard continuous-time and discrete-time semantics [12, 13], but it turns out to be decidable if only bounded execution fragments of timed automata are concerned in the context of the discrete-time semantics [36]. In this paper, we prove that this problem is still decidable in the continuous-time semantics, although it is well-known that model-checking Duration Calculus with the continuous-time semantics is much more complicated than the one with the discrete-time semantics. This is achieved by reduction to the validity of Quantified Linear Real Arithmetic (QLRA). Some examples are provided to illustrate the efficiency of our approach.","PeriodicalId":131076,"journal":{"name":"Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128417007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Compositional Synthesis of Interconnected Stochastic Control Systems based on Finite MDPs","authors":"Abolfazl Lavaei, S. Soudjani, Majid Zamani","doi":"10.1145/3178126.3186999","DOIUrl":"https://doi.org/10.1145/3178126.3186999","url":null,"abstract":"","PeriodicalId":131076,"journal":{"name":"Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131905922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Finding the minimal bit rate needed for state estimation of a dynamical system is a fundamental problem in control theory. In this paper, we present a notion of topological entropy, to lower bound the bit rate needed to estimate the state of a nonlinear dynamical system, with unknown bounded inputs, up to a constant error ε. Since the actual value of this entropy is hard to compute in general, we compute an upper bound. We show that as the bound on the input decreases, we recover a previously known bound on estimation entropy - a similar notion of entropy - for nonlinear systems without inputs [10]. For the sake of computing the bound, we present an algorithm that, given sampled and quantized measurements from a trajectory and an input signal up to a time bound T > 0, constructs a function that approximates the trajectory up to an ε error up to time T. We show that this algorithm can also be used for state estimation if the input signal can indeed be sensed in addition to the state. Finally, we present an improved bound on entropy for systems with linear inputs.
{"title":"State Estimation of Dynamical Systems with Unknown Inputs: Entropy and Bit Rates","authors":"Hussein Sibai, S. Mitra","doi":"10.1145/3178126.3178150","DOIUrl":"https://doi.org/10.1145/3178126.3178150","url":null,"abstract":"Finding the minimal bit rate needed for state estimation of a dynamical system is a fundamental problem in control theory. In this paper, we present a notion of topological entropy, to lower bound the bit rate needed to estimate the state of a nonlinear dynamical system, with unknown bounded inputs, up to a constant error ε. Since the actual value of this entropy is hard to compute in general, we compute an upper bound. We show that as the bound on the input decreases, we recover a previously known bound on estimation entropy - a similar notion of entropy - for nonlinear systems without inputs [10]. For the sake of computing the bound, we present an algorithm that, given sampled and quantized measurements from a trajectory and an input signal up to a time bound T > 0, constructs a function that approximates the trajectory up to an ε error up to time T. We show that this algorithm can also be used for state estimation if the input signal can indeed be sensed in addition to the state. Finally, we present an improved bound on entropy for systems with linear inputs.","PeriodicalId":131076,"journal":{"name":"Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116462793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Session details: Modeling and Verification","authors":"D. Ničković","doi":"10.1145/3258032","DOIUrl":"https://doi.org/10.1145/3258032","url":null,"abstract":"","PeriodicalId":131076,"journal":{"name":"Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114606679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The study of viability kernels can be of critical importance for the verification of control systems. A viability kernel over a set of safe states is the set of initial states for which the trajectory can be controlled so as to stay within the safe set for an indefinite amount of time. This paper investigates improvements of the rigorous method from Monnet et al. [19, 20]. This method computes an inner-approximation of the viability kernel of a continuous time control system using methods based on interval analysis. It consists of two phases: first an initial inner-approximation of the viability kernel is computed via Lyapunov-like functions; second the initial inner-approximation is improved by finding other states that can reach the inner-approximation, without exiting the safe set, using validated numerical integration. Among the improvements, we discuss an approach inspired by an interval method using barrier functions for computing a good initial inner-approximation of the viability kernel, easing the improvement phase.
{"title":"Improving validated computation of Viability Kernels","authors":"Benjamin Martin, Olivier Mullier","doi":"10.1145/3178126.3178141","DOIUrl":"https://doi.org/10.1145/3178126.3178141","url":null,"abstract":"The study of viability kernels can be of critical importance for the verification of control systems. A viability kernel over a set of safe states is the set of initial states for which the trajectory can be controlled so as to stay within the safe set for an indefinite amount of time. This paper investigates improvements of the rigorous method from Monnet et al. [19, 20]. This method computes an inner-approximation of the viability kernel of a continuous time control system using methods based on interval analysis. It consists of two phases: first an initial inner-approximation of the viability kernel is computed via Lyapunov-like functions; second the initial inner-approximation is improved by finding other states that can reach the inner-approximation, without exiting the safe set, using validated numerical integration. Among the improvements, we discuss an approach inspired by an interval method using barrier functions for computing a good initial inner-approximation of the viability kernel, easing the improvement phase.","PeriodicalId":131076,"journal":{"name":"Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131445218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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